Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations
Authors:
Martin Hadac
Affiliation:
Mathematical Institute of the University of Bonn, Beringstraße 1, D-53115 Bonn, Germany
Abstract:
We show the local in time well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili II equation for initial data in the non-isotropic Sobolev space with and . On the scale this result includes the full subcritical range without any additional low frequency assumption on the initial data. More generally, we prove the local in time well-posedness of the Cauchy problem for the following generalisation of the KP II equation:
for , , and . We deduce global well-posedness for , and real valued initial data.